What are the solutions for the equation x * (x^3) * (x – 5)?

To find the solution set of the equation x * (x³) * (x – 5) = 0, we can begin by setting the expression equal to zero:

x * (x3) * (x - 5) = 0

This equation is satisfied when any of the factors equals zero. Therefore, we will look at each factor separately:

1. x = 0: This factor provides us with one solution.
2. x³ = 0: Since x³ = 0 only when x = 0, this does not yield any new solutions.
3. x – 5 = 0: This factor gives us the solution x = 5.

To summarize, the expression x * (x³) * (x – 5) = 0 has the following solutions:

• x = 0
• x = 5

Thus, the solution set for the equation is:

{ 0, 5 }